Boundary Value Problems in Periodic Domains, a Potential Theoretic Approach

Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino
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Matteo Dalla Riva: The University of Tulsa, College of Engineering and Natural Science
Massimo Lanza de Cristoforis: Università degli Studi di Padova, Dipartimento di Matematica
Paolo Musolino: Università Ca’ Foscari Venezia, Dipartimento di Scienze Molecolari e Nanosistemi

Chapter Chapter 12 in Singularly Perturbed Boundary Value Problems, 2021, pp 483-511 from Springer

Abstract: Abstract In this chapter we consider boundary value problems for the Laplace equation in periodic domains obtained by removing a periodic set of holes from ℝ n $$\mathbb {R}^n$$ . To do so, we present a periodic version of Potential Theory based on layer potentials that are defined by replacing the fundamental solution of the Laplace equation with a periodic analog.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-76259-9_12

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DOI: 10.1007/978-3-030-76259-9_12

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